Lesson Worksheet: Approximating Radicals Mathematics • 8th Grade

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In this worksheet, we will practice approximating the square or cube root of a number and then using it to solve real-world problems.

Q1:

Daniel is trying to find which two whole numbers lie on either side of . He decides that it will be helpful to use what he has been taught about square numbers.

What is the greatest square number below 51?

What is the smallest square number above 51?

Hence, determine the two consecutive whole numbers that lies between.

A6 and 9
B8 and 9
C7 and 9
D7 and 8
E6 and 8

Q2:

By considering square numbers, determine an approximation for to the nearest whole number.

Q3:

Which of the integers below is the closest to ?

Q4:

Daniel wants to find an approximation for accurate to two decimal places. He sets up the equation and then starts using trial and improvement to find the solution as seen in the table.

		big/small
1		s
2		b
1.5		b
1.4		s
1.41
1.42
1.415

Determine the value of giving your answer accurate to three decimal places.

Hence, what is the value of accurate to two decimal places?

Q5:

Which of the following is the correct construction of on a number line by using a compass and a straightedge?

Q6:

Which of the following is the correct construction of on a number line using a compass and a straightedge?

Q7:

Without using a calculator, find two consecutive integers that lies between.

A5, 6
B6, 7
C7, 8
D4, 5

Q8:

Solve , then approximate your answer to one decimal place.

Q9:

A flashlight emits a light beam whose width at a distance of is given by . Determine, to the nearest tenth, the width of the beam 26 feet away from the flashlight.

Q10:

Which of the following numbers is closest to 5?

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